Hierarchical Multiscale Modeling Research Articles

Multiscale analysis of shear failure of thick-walled hollow cylinder in dry sand

A novel hierarchical multiscale model has been applied to simulate the thick-walled hollow cylinder tests in dry sand and to investigate the corresponding shear failures. The combined finite-element method and discrete-element method (FEM/DEM) model employs the FEM as a vehicle to advance the solution for a macroscopic non-linear boundary value problem incrementally. It is, meanwhile, free of conventional macroscopic phenomenological constitutive law, which is replaced by discrete-element simulations conducted with representative volume elements (RVEs) associated with the Gauss quadrature points of the FEM mesh. Numerical simulations proposed by the authors indicate that this multiscale approach is capable of replicating the evolution of cavity pressure during cavity expansion – before and after the onset of strain localisation – in qualitative agreement with laboratory tests. In particular, the curvilinear shear bands observed from experiments have been reproduced numerically. The information provided by the mesoscale DEM and the macroscale FEM reveals a close linkage between significant particle rotations taking place inside the dilative shear bands and the highly anisotropic microstructural attributes of the associated RVEs.

3D multiscale modeling of strain localization in granular media

A hierarchical multiscale modeling approach is used to investigate three-dimensional (3D) strain localization in granular media. Central to the multiscale approach is a hierarchical coupling of finite element method (FEM) and discrete element method (DEM), wherein the FEM is employed to treat a boundary value problem of a granular material and the required constitutive relation for FEM is derived directly from the DEM solution of a granular assembly embedded at each of the FEM Gauss integration points as the representative volume element (RVE). While being effective in reproducing the complex mechanical responses of granular media, the hierarchical approach helps to bypass the necessity of phenomenological constitutive models commonly needed by conventional FEM studies and meanwhile offers a viable way to link the macroscopic observations with their underlying microscopic mechanisms. To model the phenomenon of strain localization, key issues pertaining to the selection of proper RVE packings are first discussed. The multiscale approach is then applied to simulate the strain localization problem in a cubical specimen and a cylindrical specimen subjected to either conventional triaxial compression (CTC) or conventional triaxial extension (CTE) loading, which is further compared to a case under plane-strain biaxial compression (PBC) loading condition. Different failure patterns, including localized, bulging and diffuse failure modes, are observed and analyzed. Amongst all testing conditions, the PBC condition is found most favorable for the formation of localized failure. The CTC test on the cubical specimen leads to a 3D octopus-shaped localization zone, whereas the cylindrical specimen under CTC shows seemingly bulging failure from the outlook but rather more complex failure patterns within the specimen. The CTE test on a uniform specimen normally ends in a diffuse failure. Different micro mechanisms and controlling factors underlying the various interesting observations are examined and discussed.

Helium segregation on surfaces of plasma-exposed tungsten

We report a hierarchical multi-scale modeling study of implanted helium segregation on surfaces of tungsten, considered as a plasma facing component in nuclear fusion reactors. We employ a hierarchy of atomic-scale simulations based on a reliable interatomic interaction potential, including molecular-statics simulations to understand the origin of helium surface segregation, targeted molecular-dynamics (MD) simulations of near-surface cluster reactions, and large-scale MD simulations of implanted helium evolution in plasma-exposed tungsten. We find that small, mobile Hen (1 ⩽ n ⩽ 7) clusters in the near-surface region are attracted to the surface due to an elastic interaction force that provides the thermodynamic driving force for surface segregation. This elastic interaction force induces drift fluxes of these mobile Hen clusters, which increase substantially as the migrating clusters approach the surface, facilitating helium segregation on the surface. Moreover, the clusters’ drift toward the surface enables cluster reactions, most importantly trap mutation, in the near-surface region at rates much higher than in the bulk material. These near-surface cluster dynamics have significant effects on the surface morphology, near-surface defect structures, and the amount of helium retained in the material upon plasma exposure. We integrate the findings of such atomic-scale simulations into a properly parameterized and validated spatially dependent, continuum-scale reaction-diffusion cluster dynamics model, capable of predicting implanted helium evolution, surface segregation, and its near-surface effects in tungsten. This cluster-dynamics model sets the stage for development of fully atomistically informed coarse-grained models for computationally efficient simulation predictions of helium surface segregation, as well as helium retention and surface morphological evolution, toward optimal design of plasma facing components.

Developments of New Sheet Metal Forming Technology and Theory in China

Developments of new sheet metal forming technology and theory in China are reviewed in detail in this paper. Advances of crystal plasticity on the deformation mechanism of Mg alloy are firstly described, especially its applications on the prediction of sheet forming process. Then, a new macroscopic constitutive model is introduced, which possesses an enhanced description capacity of tension/compression anisotropy and anisotropic hardening. In order to take into account the twinning process of hexagonal close-packed material, a modified hierarchical multi-scale model is also established with adequate accuracy in a shorter computational time. The advanced forming limit of sheet metal, mainly about aluminum alloy, is also investigated. Besides the above theory developments, some new sheet metal forming technologies are reviewed simultaneously. The warm forming technology of Mg alloy is discussed. New processes to form sheet parts and to bend tubes are proposed by using hard granules. On the other hand, a new kind of ultra-high-strength steel based on typical 22MnB5 by introducing more residual austenite and Cu-rich phase to increase the elongation and strength and its novel forming method that integrates hot stamping and quenching participation are proposed. Progresses in sheet hydroforming, press forging and electromagnetic forming of sheet metal parts are also summarized.

Multiscale modeling of macroscopic and microscopic residual stresses in metal matrix composites using 3D realistic digital microstructure models

This work presents a hierarchical multiscale method for predicting accurately and efficiently the macroscopic and microscopic residual stresses (RSes) in MMCs based on large-size realistic digital microstructure models. Effects of various conditions on the multiscale modeling are systematically studied. Results indicate that the hierarchical multiscale model shows both a good self-consistency and a good accuracy. Compared with the kinematic uniform boundary conditions, the static uniform boundary conditions lead to more accurate prediction of the thermal misfit RS. The size of the volume element has significant effects on the predicted values of the thermal misfit RS. The hierarchical multiscale model gains significant advantages over the hybrid-semiconcurrent one with respect to both computational efficiency and computer memory cost. The local fluctuation profiles and total variations of the total RS are dominated by those of the thermal misfit RS at the microscale and by those of the macroscopic RS at the macroscale, respectively.

Multiscale modeling of droplet interface bilayer membrane networks.

Droplet interface bilayer (DIB) networks are considered for the development of stimuli-responsive membrane-based materials inspired by cellular mechanics. These DIB networks are often modeled as combinations of electrical circuit analogues, creating complex networks of capacitors and resistors that mimic the biomolecular structures. These empirical models are capable of replicating data from electrophysiology experiments, but these models do not accurately capture the underlying physical phenomena and consequently do not allow for simulations of material functionalities beyond the voltage-clamp or current-clamp conditions. The work presented here provides a more robust description of DIB network behavior through the development of a hierarchical multiscale model, recognizing that the macroscopic network properties are functions of their underlying molecular structure. The result of this research is a modeling methodology based on controlled exchanges across the interfaces of neighboring droplets. This methodology is validated against experimental data, and an extension case is provided to demonstrate possible future applications of droplet interface bilayer networks.

Multiscale modeling of effective electrical conductivity of short carbon fiber-carbon nanotube-polymer matrix hybrid composites

Epoxy matrix reinforced with conventional microscale short carbon fibers (SCFs) and carbon nanotubes (CNTs) form a hybrid material system where the characteristic length scales of SCFs and CNTs differ by multiple orders of magnitude. Several recent studies show that the addition of CNTs into a non-conducting polymer matrix improves both structural performance such as modulus, strength and fracture toughness and functional response such as electrical and thermal conductivities of the resulting nano-composite. In this study, a physics-based hierarchical multiscale modeling approach is presented to calculate the effective electrical conductivity of SCF-CNT-polymer hybrid composites. A dual step procedure is adopted to couple the effects of nano- and micro-scale so as to estimate the effective electrical properties of the composite. First, CNTs are dispersed into the non-conducting polymer matrix to obtain an electrically conductive CNT-epoxy composite. The effective electrical conductivity of CNT-epoxy composite is modeled using a physics-based formulation for both randomly distributed and vertically aligned cases of CNTs and the results are verified with the measured data available in the literature. In the second step, SCFs are randomly distributed in the CNT-epoxy composite and the effective electrical conductivity of the resulting SCF-CNT-epoxy hybrid composite is estimated using a micromechanics based self-consistent approach considering SCFs as microscopic inhomogeneities.

A Multiscale Model for the Quasi-Static Thermo-Plastic Behavior of Highly Cross-Linked Glassy Polymers

We present experimentally validated molecular dynamics predictions of the quasi-static yield and postyield behavior for a highly cross-linked epoxy polymer under general stress states and for different temperatures. In addition, a hierarchical multiscale model is presented where the nanoscale simulations obtained from molecular dynamics were homogenized to a continuum thermoplastic constitutive model for the epoxy that can be used to describe the macroscopic behavior of the material. Three major conclusions were achieved: (1) the yield surfaces generated from the nanoscale model for different temperatures agree well with the paraboloid yield criterion, supporting previous macroscopic experimental observations; (2) rescaling of the entire yield surfaces to the quasi-static case is possible by considering Argon’s theoretical predictions for pure compression of the polymer at absolute zero temperature; (3) nanoscale simulations can be used for an experimentally free calibration of macroscopic continuum models, opening new avenues for the design of materials and structures through multiscale simulations that provide structure–property–performance relationships.

Mechanical properties of graphene nanoplatelet/carbon fiber/epoxy hybrid composites: Multiscale modeling and experiments

Because of the relatively high specific mechanical properties of carbon fiber/epoxy composite materials, they are often used as structural components in aerospace applications. Graphene nanoplatelets (GNPs) can be added to the epoxy matrix to improve the overall mechanical properties of the composite. The resulting GNP/carbon fiber/epoxy hybrid composites have been studied using multiscale modeling to determine the influence of GNP volume fraction, epoxy crosslink density, and GNP dispersion on the mechanical performance. The hierarchical multiscale modeling approach developed herein includes Molecular Dynamics (MD) and micromechanical modeling, and it is validated with experimental testing of the same hybrid composite material system. The results indicate that the multiscale modeling approach is accurate and provides physical insight into the composite mechanical behavior. Also, the results quantify the substantial impact of GNP volume fraction and dispersion on the transverse mechanical properties of the hybrid composite while the effect on the axial properties is shown to be insignificant.

On large deformation granular strain measures for generating stress–strain relations based upon three-dimensional discrete element simulations

Generating stress–strain relations based upon three-dimensional discrete element simulations, for hierarchical multiscale constitutive modeling of granular materials at finite strain, requires measures of stress and strain in the reference and current configurations. The Cauchy stress tensor calculated from interparticle forces and branch vectors resulting from discrete element simulations, is well-established, but the various finite strain definitions existing in the literature are not as well studied or accepted. Thus, the paper develops seven finite strain measures in three-dimensions (Cartesian coordinates assumed): two are calculated in the reference configuration, and five are calculated in the current configuration. In the process, a time-integrated deformation gradient is formulated, with which the Cauchy stress tensor can be mapped to either the Kirchhoff stress, first Piola–Kirchhoff stress, or second Piola–Kirchhoff stress. The difficulty in calculating strain measures for granular materials is the discrete particulate nature of the materials. In the paper, strain measures are motivated by the equivalent continuum method, but are extended to finite strain in three-dimensions. Simulations are conducted to test the finite strain measures, and it is found that these strain measures are independent of rigid body rotation of a particle assembly. Granular Cauchy stress is also calculated for these discrete element simulations to be able to plot stress–strain curves in the current configuration. Finally, two numerical examples with large deformation are simulated: (1) cavity expansion, and (2) pile penetration; and their results are analyzed.

Hierarchical analysis and multi-scale modelling of rat cortical and trabecular bone.

The aim of this study was to explore the hierarchical arrangement of structural properties in cortical and trabecular bone and to determine a mathematical model that accurately predicts the tissue's mechanical properties as a function of these indices. By using a variety of analytical techniques, we were able to characterize the structural and compositional properties of cortical and trabecular bones, as well as to determine the suitable mathematical model to predict the tissue's mechanical properties using a continuum micromechanics approach. Our hierarchical analysis demonstrated that the differences between cortical and trabecular bone reside mainly at the micro- and ultrastructural levels. By gaining a better appreciation of the similarities and differences between the two bone types, we would be able to provide a better assessment and understanding of their individual roles, as well as their contribution to bone health overall.

Multiscale modeling of plasticity in a copper single crystal deformed at high strain rates

AbstractA hierarchical multiscale modeling approach is presented to predict the mechanical response of dynamically deformed (1100 s−1−4500 s−1) copper single crystal in two different crystallographic orientations.Anattempt has been made to bridge the gap between nano-, micro- and meso- scales. In view of this, Molecular Dynamics (MD) simulations at nanoscale are performed to quantify the drag coefficient for dislocations which has been exploited in Dislocation Dynamics (DD) regime at the microscale. Discrete dislocation dynamics simulations are then performed to calculate the hardening parameters required by the physics based Crystal Plasticity (CP) model at the mesoscale. The crystal plasticity model employed is based on thermally activated theory for plastic flow. Crystal plasticity simulations are performed to quantify the mechanical response of the copper single crystal in terms of stressstrain curves and shape changes under dynamic loading. The deformation response obtained from CP simulations is in good agreement with the experimental data.

An interfacial debonding-induced damage model for graphite nanoplatelet polymer composites

In situ tensile tests show damage initiates in polymer nanocomposites mainly by interfacial debonding. In this paper a hierarchical multiscale model is developed to study the damage initiation in the graphite nanoplatelets (GNP) reinforced polymer composites. The cohesive zone model was adopted to capture the nanofillers deboning. The results of atomic simulations of GNP pullout and debonding tests were used to obtain the traction–displacement relation for the cohesive zone model (CZM). The effects of volume fraction and aspect ratio of the GNP and the strength of the interfacial adhesion on the overall stress–strain response of the nanocomposite have been investigated. Results show that debonding has a significant effect on the overall stress–strain response of the nanocomposite when volume fraction and aspect ratio increase. The results also indicate that GNP/polymer interfacial strength plays a key role in the damage mechanism of the polymer nanocomposites.

Quantum-to-continuum prediction of ductility loss in aluminium-magnesium alloys due to dynamic strain aging.

Negative strain-rate sensitivity due to dynamic strain aging in Aluminium-5XXX alloys leads to reduced ductility and plastic instabilities at room temperature, inhibiting application of these alloys in many forming processes. Here a hierarchical multiscale model is presented that uses (i) quantum and atomic information on solute energies and motion around a dislocation core, (ii) dislocation models to predict the effects of solutes on dislocation motion through a dislocation forest, (iii) a thermo-kinetic constitutive model that faithfully includes the atomistic and dislocation scale mechanisms and (iv) a finite-element implementation, to predict the ductility as a function of temperature and strain rate in AA5182. The model, which contains no significant adjustable parameters, predicts the observed steep drop in ductility at room temperature, which can be directly attributed to the atomistic aging mechanism. On the basis of quantum inputs, this multiscale theory can be used in the future to design new alloys with higher ductility.

Multiscale modeling of damage progression in nylon 6/clay nanocomposites

Abstract A hierarchical multiscale model for nylon 6/clay nanocomposites is adopted to study its damage and post-damage behavior. The 3D representative volume element (RVE) of the nanocomposites at the macroscale comprises a nylon 6 matrix with embedded silicate layers. Taking into consideration the interactions between nylon 6 and the clay particulates, a gallery inter-layer was inserted between the intercalated silicate layers and an interphase layer was added around the silicate. Both gallery and interphase layers were treated as interfaces in this study. Molecular dynamics (MD) simulations were performed to obtain the material behavior of the interfaces. Results from the MD simulations were used to parameterize a traction–separation law which was incorporated into the RVE to model interfacial degradation. The damage of bulk nylon 6, on the other hand, was governed by the Gurson–Tvergaard–Needleman (GTN) model. The finite element method (FEM) was used to simulate the RVE model under quasi-static uniaxial stress loading. The constitutive relationship and fracture patterns of the nylon 6/clay model with 2.5% weight fraction of clay were studied. The apparent yield stress is found to increase while the ductility decreases when the clay particle size increases or the number of silicate layers decreases. The effect of interfacial strength on the properties of the nanocomposites is also presented. When the interfacial strength was relatively low, debonding of the interphase layer is the cause for damage initiation; a higher cohesive strength of the interfaces will lead to damage initiation from the polymer matrix around the interphase layer. This is due to inherent weak adhesion strength of the polymer chains, which was also observed through experimental results.

Interfacial and Strain Energy Analysis from <i>Ab Initio</i> Based Hierarchical Multi-Scale Modelling: The Al-Mg-Si Alloy β'' Phase

Precipitate-host lattice interface studies have not traditionally been viewed as requiring hybrid model schemes for accurate determination of the interfacial and strain energies. On the other hand, the interfaces of main hardening precipitates of age hardenable alloys are often characterized by both high levels of coherency and considerable subsystem misfits. Near the interface, linear elasticity theory evidently fails in such cases to fully correctly predict the subsystem strains. Further, density functional theory based studies on isolated supercells may prove inadequate in capturing strain influences on the chemical interactions underlying the interfacial energy. Recent work within the group has focussed on the implementation of a first principles based hierarchical multi-scale model scheme, capable of determining the interfacial and strain energies for the same model system. Choosing the fully coherent Al-Mg-Si alloy main hardening phase β'' as our test system and limiting our studies to 2D, we discuss the variation in these energies with changing precipitate cross-section morphology and size.

3D modelling of β′′ in Al–Mg–Si: Towards an atomistic level ab initio based examination of a full precipitate enclosed in a host lattice

We extend a first principles based hierarchical multi-scale model scheme for describing a fully coherent precipitate in a host lattice to 3D simulations. As our test system, the needle-shaped main hardening Al–Mg–Si alloy precipitate β′′ is chosen. We show that computational costs do not impose practical limits on the modelling: the scheme can probe the full interface energy for physically sized and well isolated precipitates. Examining a series of energetically competitive bulk β′′ configurations, we highlight a series of results: (i) the scatter in the structural parameters for different β′′ configurations clearly exceeds experimental uncertainties also when interaction with the host lattice is taken into account. (ii) Structural and compositional β′′/Al interfaces generally coincide. This implies that precipitate stoichiometry is retained only for the two β′′ configurations with the lowest formation energy (compositions Mg5Al2Si4, Mg4Al3Si4). (iii) β′′–Mg4Al3Si4 emerges as a minimum energy configuration for large precipitates. Finally, (iv) more complete modelling, with precipitates surrounded by Al in all three dimensions, is expected to highlight a non-negligible influence of the precipitate misfit along the main growth (needle) direction.

An efficient multiscale model of damping properties for filled elastomers with complex microstructures

This work proposes an efficient framework for prediction of filled elastomer damping properties based on imaged microstructures. The efficiency of this method stems from a hierarchical multiscale modeling scheme, in which the constitutive response of subcell regions, smaller than a representative volume element (RVE), are determined using micromechanics; the resulting constitutive parameters then act as inputs to finite element simulations of the RVE, from which damping properties are extracted. It is shown that the micromechanics models of Halpin–Tsai and Mori–Tanaka are insufficient for modeling subcells with many filler clusters, and thus these models are augmented by an additional interaction term, based on stress concentration factors. The multiscale framework is compared to direct numerical simulations in two dimensions and extended to predictions for three dimensional systems, which include the response of matrix–filler interphase properties. The proposed multiscale framework shows a significant improvement in computational speed over direct numerical simulations using the finite element method, and thus allows for detailed parametric studies of microstructural properties to aid in the design of filled elastomeric systems.

Interface configuration stability and interfacial energy for the β″ phase in Al–Mg–Si as examined with a first principles based hierarchical multi-scale scheme

We examine interface configuration stabilities and determine interfacial energies over the full precipitate cross-section for the needle-shaped main hardening phase β″ in the Al–Mg–Si alloy system. Our supercell based studies are performed within the framework of density functional theory, hence providing first principles accuracy for the electronic structure. In addition, each cell is distorted according to information from a hierarchical multi-scale model scheme, implying that also the local ionic structure is mimicked throughout. Making use of the larger structural freedom available compared to an isolated supercell based approach, we propose a modified expression for deriving the interfacial energy. When examined for an average sized β″-Mg5Al2Si4 precipitate, this expression provides non-negligible changes to the interfacial energies, exceeding 20% for one interface. We further argue that a full hybrid scheme would likely influence the energies non-negligibly, with a dependence on the precipitate dimensions appearing plausible. Additional modification of the interfacial energy expression for implementation in such a scheme is discussed. Our calculations suggest stability of the structural interface configuration, compatible with a stoichiometric precipitate for the chosen bulk phase composition, over the entire interface.

Modeling and simulation of the water gradient within a Nafion membrane

The perfluorinated sulfonic acid membrane (Nafion) shows among ionomers high water uptake and cationic conductivity. These properties allow Nafion to be used in nanocomposite actuators, sensors and fuel cells. In situ experiments have shown that there is a water gradient within the Nafion membrane. The water gradient causes the alteration of other physical properties within the thickness of the membrane and has a drastic impact on the performance of the devices made of the Nafion membrane. Deriving closed-form equations and using molecular dynamics (MD) simulation results, we bridge Nafion properties at the atomic scale and the macroscopic behavior of the membrane within a hierarchical multi-scale model. Multiple discrete simulation cells are selected across the thickness of the membrane with a wide range of water contents as representative volume elements (RVEs). The present framework is able to quantitatively predict the macroscopic properties of Nafion with the nanometric resolution regarding the water gradient across the membrane.